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A random variable $X$ has the density function

$f(x)= \begin{Bmatrix} c(x+\sqrt{x}) & x\epsilon [0,1]\\ 0& otherwise \end{Bmatrix}.$

(a)  Determine c.
in Probability by Boss (10.9k points) | 46 views
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$P(0 \leq x \leq 1) =$ $\large \int_{0}^{1} c(x \ + \sqrt x)$

$1 =$ $\large c \left [ \frac{x^2}{2} + \frac{2 x^{3/2}}{3} \right ]_{0}^{1}$

$1 =$$\Large c\left [ \frac{1}{2} + \frac{2 }{3} \right ]$

$c =$$\large \frac{6}{7}$
by Boss (36.8k points)
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